# solve the inequality using an appropriate property of the absolute value. Provide an exact answer using interval notation?

Any help would be appreciated!

Relevance
• ted s
Lv 7
1 month ago

2 false "answers" because of carelessness....you have 5 < 7 | x/8 - 3 |...multiply everything by ' 8 '......40 < 7 | x - 24 | these all all reals which are (40/7) units away from  24.........( - ∞ , 24 - 40/7) U ( 24 + 40/7 , ∞)....so you should look at the other 2 and find the careless errors...it will help you later on when doing problems

• Bryce
Lv 7
1 month ago

-7|(1/8)x - 3| + 9< 4

-7|(1/8)x - 3|< -5

|(1/8)x - 3|> 5/7

-5/7>(1/8)x - 3>5/7

16/7>(1/8)x>26/7

128/7>x>208/7

• 1 month ago

First simplify equation

-7 * abs(X/8 - 3) + 9 < 4

-7 * abs(X/8 - 3) < -5

abs( X/8 - 3) > 5/7  (must flip inequality when dividing or multiplying by negative)

Then abs means that amount can be positive or negative so

1) X/8 - 3 > 5/7  and

2) -(X/8 - 3) > 5/7

2) becomes X/8 - 3 < -5/7

so -5/7 < X/8 - 3 < 5/7

and

-5 < X * 7/8 - 21 < 5  add 21 to all parts

16 < X * 7/8 < 26  multiply by 8/7

16 * 8 / 7 < X < 26 * 8 / 7

Is this enough?